The existence and stability for weakly Ky Fan’s points of set-valued mappings

Abstract In this paper, the notion of weakly Ky Fan’s points of set-valued mappings is established, and we prove some existence theorems of weakly Ky Fan’s points for functions with no continuity or space with no compactness. Then, from the viewpoint of the essential stability, we prove that most of problems in weakly Ky Fan’s points (in the sense of Baire category) are essential. MSC:26D20, 26E25.